you and a companion are driving a lonely stretch of road in a car with a speedometer but no odometer. to…

Explanation:

Step1: Recall left - endpoint Riemann sum formula

The left - endpoint Riemann sum for approximating the distance $d$ (where distance $d=\int_{a}^{b}v(t)dt$ and $v(t)$ is velocity as a function of time $t$) is given by $L_n=\sum_{i = 0}^{n - 1}v(t_i)\Delta t$, where $\Delta t$ is the time interval between measurements and $v(t_i)$ are the left - endpoint velocities. Here, $\Delta t=10$ s.

Step2: Identify the left - endpoint velocities

The left - endpoint velocities for the intervals are: $v(0) = 0$, $v(10)=20$, $v(20)=14$, $v(30)=27$, $v(40)=43$, $v(50)=33$, $v(60)=13$, $v(70)=22$, $v(80)=21$, $v(90)=30$, $v(100)=28$, $v(110)=40$, $v(120)=48$.

Step3: Calculate the sum

[ \begin{align*} L_{13}&=10\times(0 + 20+14 + 27+43+33+13+22+21+30+28+40+48)\ &=10\times(349)\ &=3490 \end{align*} ]

Answer:

$3490$ m (assuming the velocity is in m/s)